I) consists of two loops symmetrically placed about the coordinate axes.
If the equation of this line, referred to new coordinate axes in the plane area, is written xcos a+y sin a - h=o, (3) R = f f p(h - x cos a - y sin a)dxdy, (4) zR= f fpx(h - xcos a - y sin a)dxdy, (5) yR = f f py(h - x cos a - y sin a)dxdy.
In the Eulerian notation u, v, w denote the components of the velocity q parallel to the coordinate axes at any point (x, y, z) at the time t; u, v, w are functions of x, y, z, t, the independent variables; and d is used here to denote partial differentiation with respect to any one of these four independent variables, all capable of varying one at a time.
(7) For example, in the equilateral triangle of (8) § 28, referred to coordinate axes made by the base and height, = -2 Ra,(3y/h= - 1.
- In many problems, such as the motion of a solid in liquid, it is convenient to take coordinate axes fixed to the solid and moving with it as the movable trihedron frame of reference.